soft3/zheng/docs/explanation.md

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zheng explanations

zheng is a polynomial proof system. these documents explain the concepts, design decisions, and historical context.

for formal definitions, see specs/ (soundness per component: specs/soundness.md). for the hash primitive, see hemera. for the VM whose traces we prove, see nox.

reading path

                              ╭──────── vision ────────╮
                              │                        │
                     why-zheng                the-name
                              │
                              │
                    ╭──────── foundations ────────╮
                    │            │               │
                 stark          CCS         landscape
                    │            │               │
                    ╰────────────┼───────────────╯
                                 │
                   ╭──────── protocols ────────╮
                   │             │             │
              sumcheck    poly-commits    fri-to-whir
                   │             │             │
                   ╰─────────────┼─────────────╯
                                 │
                                 │
                        superspartan
                                 │
                                 │
                           whirlaway
                                 │
                                 │
                        trace-to-proof
                                 │
                                 │
                    ╭──────── powers ──────────╮
                    │       │        │         │
              recursion  security  performance  bbg-integration

pages

vision

page topic
why-zheng why a custom proof system — what zheng enables and why existing systems fall short
the-name 証 etymology — proof as evidence, verification as witnessing

foundations

page topic
stark STARK systems — arithmetization (AIR, R1CS, CCS), univariate vs multilinear, heritage; zheng proofs are not STARKs
CCS Customizable Constraint Systems — why unified constraints matter for zheng and accumulation
landscape proof system taxonomy — trusted setup vs transparent, pre-quantum vs post-quantum, SNARKs vs STARKs vs multilinear STARKs

core protocols

page topic
sumcheck the heart of the system — reducing exponential verification to logarithmic via the sumcheck protocol
polynomial-commitments the trust anchor — commit to data, prove evaluations, bind the prover to a single polynomial
fri-to-whir the PCS evolution — FRI to STIR to WHIR, each generation's insight and what it unlocks
whir the shipped commitment of the succinct profile — protocol, parameters, measured figures
recursive-brakedown a retired design: what it was and why it was unsound

architecture

page topic
superspartan CCS as universal constraint system — why AIR matters for nox and how SuperSpartan unifies them
whirlaway the architecture of the succinct profile — how sumcheck protocol, WHIR and SuperSpartan compose
trace-to-proof from a nox program to a zheng proof: the compiled relation, the machine trace, and the retired register trace
zheng-vs-starks zheng proofs and STARK systems — shared trust model, different IOP and commitment, measured figures

powers

page topic
recursion accumulation, IVC and wrap — how a nox run of any length becomes one proof of constant size
security hash-based assumptions — post-quantum guarantees, the soundness ledger explained, no trusted setup
performance measured proof sizes and verification times per profile, against the goal
bbg-integration how a proof reads BBG state — state roots, evidence, the QueryProof migration

tooling

page topic
zippel eniac/zippel as a checker for zheng's IOPs — derived transcripts, completeness and special-soundness analyses; what it cannot cover and the first experiment

see also

  • nebu — the Goldilocks field underlying all arithmetic
  • hemera — the hash primitive used in every Merkle tree and commitment
  • nox — the VM whose execution traces zheng proves
  • BBG — the state database whose integrity proofs zheng generates

Folder

Homonyms

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